Monomial ideals establish a link between algebra and combinatorics. Since the work of David Hilbert, free resolutions have been a very important tool for understanding the properties of ideals. One of the basic questions about the resolutions of ideals is when they are linear. Reducing to monomial ideals, it is an open problem to give a necessary and sufficient condition for the ideal to have a linear resolution. In this talk, using combinatorial methods, we will give a partial answer to this problem.